doc-src/Logics/logics.bbl
author paulson
Fri Feb 16 18:00:47 1996 +0100 (1996-02-16)
changeset 1512 ce37c64244c0
parent 1444 23ceb1dc9755
child 1536 efbc887dfefb
permissions -rw-r--r--
Elimination of fully-functorial style.
Type tactic changed to a type abbrevation (from a datatype).
Constructor tactic and function apply deleted.
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\begin{thebibliography}{10}
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\bibitem{abrial93}
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J.~R. Abrial and G.~Laffitte.
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\newblock Towards the mechanization of the proofs of some classical theorems of
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  set theory.
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\newblock preprint, February 1993.
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\bibitem{andrews86}
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Peter~B. Andrews.
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\newblock {\em An Introduction to Mathematical Logic and Type Theory: To Truth
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  Through Proof}.
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\newblock Academic Press, 1986.
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\bibitem{basin91}
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David Basin and Matt Kaufmann.
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\newblock The {Boyer-Moore} prover and {Nuprl}: An experimental comparison.
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\newblock In {G\'erard} Huet and Gordon Plotkin, editors, {\em Logical
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  Frameworks}, pages 89--119. Cambridge University Press, 1991.
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\bibitem{boyer86}
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Robert Boyer, Ewing Lusk, William McCune, Ross Overbeek, Mark Stickel, and
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  Lawrence Wos.
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\newblock Set theory in first-order logic: Clauses for {G\"odel's} axioms.
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\newblock {\em Journal of Automated Reasoning}, 2(3):287--327, 1986.
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\bibitem{camilleri92}
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J.~Camilleri and T.~F. Melham.
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\newblock Reasoning with inductively defined relations in the {HOL} theorem
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  prover.
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\newblock Technical Report 265, Computer Laboratory, University of Cambridge,
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  August 1992.
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\bibitem{church40}
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Alonzo Church.
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\newblock A formulation of the simple theory of types.
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\newblock {\em Journal of Symbolic Logic}, 5:56--68, 1940.
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\bibitem{coen92}
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Martin~D. Coen.
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\newblock {\em Interactive Program Derivation}.
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\newblock PhD thesis, University of Cambridge, November 1992.
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\newblock Computer Laboratory Technical Report 272.
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\bibitem{constable86}
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R.~L. Constable et~al.
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\newblock {\em Implementing Mathematics with the Nuprl Proof Development
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  System}.
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\newblock Prentice-Hall, 1986.
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\bibitem{davey&priestley}
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B.~A. Davey and H.~A. Priestley.
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\newblock {\em Introduction to Lattices and Order}.
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\newblock Cambridge University Press, 1990.
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\bibitem{devlin79}
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Keith~J. Devlin.
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\newblock {\em Fundamentals of Contemporary Set Theory}.
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\newblock Springer, 1979.
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\bibitem{dummett}
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Michael Dummett.
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\newblock {\em Elements of Intuitionism}.
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\newblock Oxford University Press, 1977.
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\bibitem{dyckhoff}
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Roy Dyckhoff.
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\newblock Contraction-free sequent calculi for intuitionistic logic.
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\newblock {\em Journal of Symbolic Logic}, 57(3):795--807, 1992.
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\bibitem{felty91a}
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Amy Felty.
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\newblock A logic program for transforming sequent proofs to natural deduction
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  proofs.
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\newblock In Peter Schroeder-Heister, editor, {\em Extensions of Logic
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  Programming}, LNAI 475, pages 157--178. Springer, 1991.
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\bibitem{frost93}
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Jacob Frost.
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\newblock A case study of co-induction in {Isabelle HOL}.
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\newblock Technical Report 308, Computer Laboratory, University of Cambridge,
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  August 1993.
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\bibitem{gallier86}
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J.~H. Gallier.
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\newblock {\em Logic for Computer Science: Foundations of Automatic Theorem
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  Proving}.
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\newblock Harper \& Row, 1986.
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\bibitem{mgordon-hol}
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M.~J.~C. Gordon and T.~F. Melham.
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\newblock {\em Introduction to {HOL}: A Theorem Proving Environment for Higher
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  Order Logic}.
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\newblock Cambridge University Press, 1993.
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\bibitem{halmos60}
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Paul~R. Halmos.
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\newblock {\em Naive Set Theory}.
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\newblock Van Nostrand, 1960.
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\bibitem{huet78}
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G.~P. Huet and B.~Lang.
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\newblock Proving and applying program transformations expressed with
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  second-order patterns.
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\newblock {\em Acta Informatica}, 11:31--55, 1978.
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\bibitem{kunen80}
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Kenneth Kunen.
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\newblock {\em Set Theory: An Introduction to Independence Proofs}.
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\newblock North-Holland, 1980.
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\bibitem{alf}
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Lena Magnusson and Bengt {Nordstr\"om}.
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\newblock The {ALF} proof editor and its proof engine.
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\newblock In Henk Barendregt and Tobias Nipkow, editors, {\em Types for Proofs
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  and Programs: International Workshop {TYPES '93}}, LNCS 806, pages 213--237.
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  Springer, published 1994.
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\bibitem{mw81}
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Zohar Manna and Richard Waldinger.
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\newblock Deductive synthesis of the unification algorithm.
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\newblock {\em Science of Computer Programming}, 1(1):5--48, 1981.
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\bibitem{martinlof84}
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Per Martin-L\"of.
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\newblock {\em Intuitionistic type theory}.
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\newblock Bibliopolis, 1984.
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\bibitem{milner-coind}
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Robin Milner and Mads Tofte.
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\newblock Co-induction in relational semantics.
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\newblock {\em Theoretical Computer Science}, 87:209--220, 1991.
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\bibitem{noel}
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Philippe No{\"e}l.
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\newblock Experimenting with {Isabelle} in {ZF} set theory.
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\newblock {\em Journal of Automated Reasoning}, 10(1):15--58, 1993.
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\bibitem{nordstrom90}
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Bengt {Nordstr\"om}, Kent Petersson, and Jan Smith.
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\newblock {\em Programming in {Martin-L\"of}'s Type Theory. An Introduction}.
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\newblock Oxford University Press, 1990.
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\bibitem{paulin92}
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Christine Paulin-Mohring.
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\newblock Inductive definitions in the system {Coq}: Rules and properties.
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\newblock Research Report 92-49, LIP, Ecole Normale Sup\'erieure de Lyon,
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  December 1992.
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\bibitem{paulson85}
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Lawrence~C. Paulson.
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\newblock Verifying the unification algorithm in {LCF}.
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\newblock {\em Science of Computer Programming}, 5:143--170, 1985.
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\bibitem{paulson87}
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Lawrence~C. Paulson.
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\newblock {\em Logic and Computation: Interactive proof with Cambridge LCF}.
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\newblock Cambridge University Press, 1987.
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\bibitem{paulson-coind}
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Lawrence~C. Paulson.
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\newblock Co-induction and co-recursion in higher-order logic.
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\newblock Technical Report 304, Computer Laboratory, University of Cambridge,
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  July 1993.
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\newblock To appear in the Festscrift for Alonzo Church, edited by A. Anderson
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  and M. Zeleny.
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\bibitem{paulson-set-I}
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Lawrence~C. Paulson.
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\newblock Set theory for verification: {I}. {From} foundations to functions.
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\newblock {\em Journal of Automated Reasoning}, 11(3):353--389, 1993.
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\bibitem{paulson-CADE}
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Lawrence~C. Paulson.
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\newblock A fixedpoint approach to implementing (co)inductive definitions.
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\newblock In Alan Bundy, editor, {\em Automated Deduction --- {CADE}-12}, LNAI
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  814, pages 148--161. Springer, 1994.
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\newblock 12th international conference.
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\bibitem{paulson-set-II}
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Lawrence~C. Paulson.
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\newblock Set theory for verification: {II}. {Induction} and recursion.
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\newblock {\em Journal of Automated Reasoning}, 15(2):167--215, 1995.
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\bibitem{paulson-COLOG}
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Lawrence~C. Paulson.
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\newblock A formulation of the simple theory of types (for {Isabelle}).
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\newblock In P.~Martin-L\"of and G.~Mints, editors, {\em COLOG-88:
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  International Conference on Computer Logic}, LNCS 417, pages 246--274,
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  Tallinn, Published 1990. Estonian Academy of Sciences, Springer.
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\bibitem{paulson-final}
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Lawrence~C. Paulson.
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\newblock A concrete final coalgebra theorem for {ZF} set theory.
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\newblock In Peter Dybjer, Bengt Nordstr{\"om}, and Jan Smith, editors, {\em
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  Types for Proofs and Programs: International Workshop {TYPES '94}}, LNCS 996,
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  pages 120--139. Springer, published 1995.
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\bibitem{pelletier86}
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F.~J. Pelletier.
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\newblock Seventy-five problems for testing automatic theorem provers.
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\newblock {\em Journal of Automated Reasoning}, 2:191--216, 1986.
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\newblock Errata, JAR 4 (1988), 235--236.
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\bibitem{plaisted90}
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David~A. Plaisted.
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\newblock A sequent-style model elimination strategy and a positive refinement.
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\newblock {\em Journal of Automated Reasoning}, 6(4):389--402, 1990.
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\bibitem{quaife92}
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Art Quaife.
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\newblock Automated deduction in {von Neumann-Bernays-G\"odel} set theory.
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\newblock {\em Journal of Automated Reasoning}, 8(1):91--147, 1992.
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\bibitem{suppes72}
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Patrick Suppes.
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\newblock {\em Axiomatic Set Theory}.
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\newblock Dover, 1972.
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\bibitem{takeuti87}
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G.~Takeuti.
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\newblock {\em Proof Theory}.
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\newblock North-Holland, 2nd edition, 1987.
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\bibitem{thompson91}
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Simon Thompson.
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\newblock {\em Type Theory and Functional Programming}.
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\newblock Addison-Wesley, 1991.
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\bibitem{principia}
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A.~N. Whitehead and B.~Russell.
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\newblock {\em Principia Mathematica}.
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\newblock Cambridge University Press, 1962.
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\newblock Paperback edition to *56, abridged from the 2nd edition (1927).
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\bibitem{winskel93}
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Glynn Winskel.
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\newblock {\em The Formal Semantics of Programming Languages}.
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\newblock MIT Press, 1993.
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\end{thebibliography}